Gavarret was born on May 11, 1956, in Minas, Lavalleja, Uruguay. He earned an MBA degree from Instituto Nacional de Pos-Graduacao in Campinas, Brazil. He was previously trained in management at the Escuela Superior de Administracion Empresas. He worked as the general manager of a pharmaceutical company , GP Pharm S.A., in Peru. He also worked for that company as a regional manager for Central America and Uruguay. He worked as general manager for Peru and business director for Brazil for the IVAX Corporation. He worked for Tecnofarma for 18 years.
He served as a full-time missionary in Paraguay and Uruguay. He has also served as a bishop, stake president, Area Authority, and a member of the Fourth Quorum of the Seventy. He has served as president of the Paraguay Asuncion Mission.
Gavarret was part of the historic 184th Semiannual General Conference (2014) where four members of the First Quorum of the Seventy addressed the audience in their native languages, with either English subtitles or translation. Gavarret spoke in Spanish in the Saturday afternoon session.
He married Norma Beatriz Gorgoroso and they are the parents of three children.